SMOOTHING QUANTILE REGRESSION WITH ELASTIC NET PENALTY

摘要

High-dimensional data are commonly encountered in various scientific fields, such as information technology, biology, economics and so on. This poses great challenges to modern statistical analysis and optimal computation. First, the high dimensionality often induces the collinearity of variables. Second, the error of high-dimensional data may be heavy-tailed. In order to deal with these two issues, we introduce the penalized quantile regression with the elastic net penalty that combines the strengths of the quadratic regularization and the lasso shrinkage. By smoothing quantile loss function with the Huber smooth function, we give the smoothing quantile regression with elastic net penalty (SQEN). In this model, the regularizer which leads to a grouping effect can treat collinearity well and the Huber smooth loss is suitable for heavytailed data. In high-dimensional setting, we derive the statistical consistent property of the SQEN estimator. To make the SQEN practically feasible, we propose an efficient iterative SQEN-MM method and establish its global convergence. From numerical results, we can see our method can solve SQEN model efficiently and effectively.